Inductance device



Nov. 2 1926.. 1,604,996

1.. R. GUILBAU'D INDUGTANCE DEvIEl Filed June 2o, 1924 Patented Nov. 2, 1926.

UNITED -sTATEs PATENT OFFICE.

LUCIEN RL GUILBAUD, OF NEW YORK, N. Y., ASSIGNOR TO WESTERN ELECTRIC COM- PANY, INCORPORATED, OF NEW YORK, N. A CORPORATION F NEW YORK.

INDUCTANCE DEVICE This invention relates -to inductance devices of the type known in the art as retard C. resistance within reasonable coils, transformers and the like, and particularly to shell-type magnetic cores for such devices. y

yAn object of the invention is to improve the efciency of magneticcores of the general type referred to.

More specifically the invention has for its object. to produce a shell-type core having such a shape and such dimensions las to give the maximum inductance fora given overall area of lamination.

In the design of transformers for many purposes, such as telephony and the like, the essential points ,to be considered are: the inductance of the lcoil, its D. C. resistance, its magnetic' leakage andthe distributed capacity of the winding. It is generally necessary to consider all of the above factors in the design of transformers to meet the particular circuit requirements as to load, impedance, etc., while in the case of retard coils, the problemof obtaining the maximum ratio of reactance to D. C. resistance is most essential. In input'thansformers for vacuum tubes, however, it is well known that the D. C. resistance of the secondary wind- .ing is unimportant and that in all cases the smallest lsize of wire available ycan be used, the tube impedance being so high that the D.` Cl resistance of the secondary winding is negligible. While in special cases, .as in the case of input transformers, the D. C. resistance need'not be considered, as agenleral proposition, oneof the main considerations in transfofr desii stle/ problem of obtaining a given in uctance with the smallest possible D. C. resistance. Hence in designing a new `type of transformer, it is often, if not generally advisable to design it so that it will give a suicientinductance to be useful as an inputv transformer, and, at the same time, have the D. limitsv so that efficient transformers for other uses and retard coils may be wound on thesame4v design of core.

yIn accordance with the invention, 1t has been found that the most advantageous proportions of a shell-type core for securing a maximum inductance for a given overall area of lamination are obtained when the window apertures or winding spaces are sgiare having a dimension of 0.8X on a s1 e, apertures is 0L150X, and the distance between the Window apertures and the adjacent outer sides of the lamination is 0.125X, where X is one-half the length of the longest side of the lamination.

The principal features and objects of the invention will be clear' from the following detailed description read in connection lwith the accompanying drawings.

In the drawings,lFig. 1 shows a transformer having a core of the general type ofthe invention, Fig. 2 shows the dimensional notation used in the specification, Fig. 3 shows the most advantageousdimensions of a core as embodied in the invention, Fig, 4 is a curve showing the relation between the constant K of Fig. 2 and the.

inductanoe, and Fig. 5 shows a section along the line. 5-5 of Fig. 2. Like parts bear like reference characters throughout the several drawings. Referring to Fig. 1 a transformer is shown comprising a laminated, shell-type core 1 having' outer branches 2 and central Vbranch 3, primary winding 4 and secondary winding l5. Fig. 2 shows a plan view of a lamination of thecore 1 indicating the dimensional notation which will be used in the description.' Thedimensions are` a referred to the half llength X of the lamination, the window' 6 having a dimension KX lengthwise of thelamination, the remainder (1 -K) AX being distributed between the solid branches A2 and 3, a part a {1T-K) X in the center branch and the remainder (1 -a) (1K)' X in one of the outer branches.

If we consider the core 1 as a lamination having a thickness ofl unity, the magnetlc permeability being p. for a given number of turns N in the winding the inductance win be where A1l is thejarea of a vertical section through the central branch 3 ofthe core the distance between the window.

along the line 5 5, as shown in 'Fig. 5; A2 is twice the area of a vertical section through either outer branch 2 of the core along the line 5--5, as shown in Fig. 5; the two outer branches 2 of the core being considered as one branch of double area; Z1 the. mean length of the portion of the magnetic circuit Within the center branch 3, and Z2 the mean length of the portion of the magnetic circuit Within one of the outer branches 2;

It is assumed that the area A1 of the cross section of the central 'branch 3 of the core is uniform between the lines 7-9 and 8-10, and that the outer branch 2 of the core is also of uniform cross section.

As a first step in determining the most eiiicient dimensions of the'core for a given inductance, the area of the window 6 is assumed to be a constant and the relationship between the two cross 'sections A1 and A2 is determined. The best shape of window will be that which for a given number of turns in the winding will offer the shortest length of. magnetic path. Now for all coils wound on a spool it is necessary to use a rectangular window. It is well known that 4and I of all rectangular figures the square offers the largest area for a given perimeter. The factor f AiAz Z1A2+Z2A1 i of equation (l) reduces to 1% if l1=l2 =vl,

which means that if the two cross-sections A, and A2 are equal for the central and outer branches, the ideal window would be square. If Z1 differs from Z2, this is no longer strictly true. However, a square window will be assumed as an approximation. The result obtained will show that Z1 is very little different from Z2 and that the approximation is justified. Then, referring to'Fig. 2, as. the .thickness of the core is unity, it is apparent that l Ai:`2a(1-K)X (2) @22u-a) (1 K)x (a) Substitutin equations (2) and in equation (l), l disappears and equation(l) reduces to f and window, will be determined. To determine the maximum of L when a varies, the variable part of equation (4) will be studied. This 1s Y a(1 a) (1-a+aK)(1-a) +(2+K)a The derivative of this expression with respect to a is [am -K) +2aK+ 1](1-2a)a(1a)[2a(1 -K)+2K] [aiu-K) -i-ZaK-l-l]2 Making the numerator -a2(K-}-1)-2a{1: 0, and solving, two roots are obtained for values of a between which the derivative of equation (3) with respect to a will be positive, namely JLM iK-t1) The highervalue,

WAM/m =2(1-a+aK)(1-a)(1-K)+(2+K). 2a(1-K) 4) Holding N constant, the location of the:

reducing to-` 0,2(1 K) +2aK +1 (5) l mately a squarexand Z2 may be replaced by SI1.v Then, equation (4) lwill take the form X will be assumed to be constant. Then, L will be a maximum when K4(1-K) maximunnthat is, When Solving equation (10), an approximate value 1s for K is obtained.

Kzos l (11) Substituting this'value of K in e nation '(8) a corresponding value for a is 'o The values of K and a havinglheen determined, the complete shape of thelamination is known. Substituting the values 0i? K and a in. the dimensional units'shown in Fig. 2, we will obtain the dimensionsf'as functions of X. The actual proportions'are shown'. in Fig. 3, the windows 6 each being 0.8K square, the central solid branch 0.15OXW Wide and all other solid branches being each 0.125X Wide;

To verify the results obtained, values of 'proportional to`the inductance, were calculated for various values of K'and plotted giving the curve shown in F ig. 4. This shows the existence of a maximum for K :0.8. The calculations show that the approximations made. in determining did not impair the accuracy of the results very much, as a variation of approximately only one per cent shows in the numerical results. Also, taking any two values for K, for instance K:0.8 and KzOA, and calculating thickness will have-to be determined a, values of la :0.373 and'a:l 0.391', res ec'- tively, are obtained. If the values of 4X4 A1A, LA: 'i' 22A-1 .corresponding these values of gz and K are calculated, the results show that they correspond to a maximum for the'pinductance L, .showin that the approximations made were justi ed.

Throughout y our calculations, we 'have assumed, a thickness of unity for the. core. v(,)alculation to determine the best thickness for the core, that is, the thickness givingv the largestV inductance for a given volume of magnetic material used, shows that the inductance 'will steadily increase vwith a decreasingv thickness of the core theoverall volume of the core being kept constant. Finally, we would have "a laminationinfinitely thin and of infinitely large area and a coill with an infinite number of turns. This not beingl practicable, the question if other considerations such as minimum D. resistance or minimum weight. lOur `two determinations', that is, (1) location of window, and (2) size of thewindow are independent of each other. If both values are applied strictly, we will obtain a shape of tained. v

'assumed and X obtained from lamination as shown in Fig. 3 andthe inductance of the coilwould thenbe given by where ,a is the permeability of the core, t the thicknessof the core in centimeters, and w theeffective cross section of the wire used expressed 1n the same units .as X, so that L being given wecan determine or Land t being given, we can determine w.

,-If'a transformer is to be designed that will give a certain inductance with the smallest possible volume, the first step will be to determine from considerations of the amount ofcurrent to be carried the smallest sizeof wire that can be used, which Will give w. Then, a probable value for t can be which is simply equation (4) in which a and K have been replaced by their numerical values. It is obvious that by varying the Adimension t, the other dimensions can beA changed correspondingly to obtain theprof portions that may be desired for appearance, convenience of mounting, etc.

" The value' of K, which determines the size of' the window, may be yvaried .from the value of 0.8 given, as' may be desired, particularly where-the relative cost of a particular core material and the wire material- 'in the windings is an important consideration. It will be noted that, as 'K is increased, the volume yof the winding will be increased and that of the core decreased.

By a simple calculation, making use of the equations given' above, the value of K which will just about 'balance the costs of the core and winding can be determined. This value of K will not be very different from the opti- -mum value of 0.18 as derived above.

It has'v been determined by calculation based on coils now in use and heretofore considered as standard that by adopting the proportions inaccordance with th1s invention, very valuable' results can be obtained.

ils

and description, a 'laminated core of the rshell-type has been shown in the drawings and referred to inthe description, the invention is applicable any other core of the ,shell-type. vThe 'shell-typecore referred to in the description and claims is the Wellknowncore having at least two winding -spaces or apertures surrounded b y a s hell comprisingv a central branch and two :outer branches. While for convenience 1n description laminations havebeen referred to,l

it isobvios that, as pointed out above, no actual laminat-ions neetlybe used but a solid or vother type of core structure can be used,

' inu which case the ylaminations may beconsidered as being present rand separatedby imaginary planes.

What is claimed is t. 1. A shellty pe core for an in ductance device, .having a central `branch and two outerbranches in shunt toeach other and in series with said central branch', said central-branch being of greater Across-section than either i outer branch but of less cross-section than both outer branches together:

(1"6) of the length ofglthe longest side .of the lamination of the core 'in len l.

3. A shell-type core of uni crm thickness as claimedin-claim l inm'which the central limb between the window'apertures has 'a width substantially 0.075 times the length of.

the longest side of the-lamination of the core.

sixteenth form thickness 4. A shell-type core olf uniform thickness as claimedin claim l in which each of the side of the lamination of the core.

5.' A shell-type core of uniform thickness as claimed in claim 1, in which the window -outer limbs has'a width substantially ,one-.-

(116') of the length-of the longest v apertures. aresqua're having sides each fourtenths (T410- the length ofthe longest side of central limb betweengsaid window apertures having -a vwidth substantially 0.075 times the length ot the longest side of the lamination'of said core, andeach of the outer limbs-of said cere having awidth substantially one-sixteenth lthelength of the :the laminat-ion ;of said core in length, the

longest side ofthe lamination of said core inlength.

outer branches,l said central branch having A shell-type core for an-inductance de? vice,comprising a centralbranch and'twc' a cross-section substantially six-tenths (1%) the cross-section of both outer branchestogether.

A shell-type core for an inductance de? vice, comprisingfacentral branch and two outerbranches, said outer branches being of' ual'section and eachjsubstantially eighttenths (1%) the cross-section of said central branch. v4

v In witness whereof, I hereunto subscribe my' name this 12th day of June A. D., 1924..`

LUCIEN R. GUILBAUD. 

